The domain of `f(x)=log_x 12` is (i) `(0,infty)` (ii ) `(0,1)cup (1,infty)` (iii) `(-infty,0)` (iv) `(2,12)`

The exhaustive values of x for which f(x) = tan^-1 x - x is decreasing is (i) (1,infty) (ii) (-1,infty) (iii) (-infty,infty) (iv) (0,infty)

If alpha , beta are the roots of the quadratic equation (p^2 + p + 1) x^2 + (p - 1) x + p^2 = 0 such that unity lies between the roots then the set of values of p is (i) O/ (ii) p in (-infty,-1) cup (0,infty) (iii) p in (-1,infty) (iv) (-1,1)

If the point (1, a) lies in between the lines x + y =1 and 2(x+y) = 3 then a lies in (i) (-infty,0)cup (1,infty) (ii) (0,1/2) (iii) (-infty,0)cup (1/2,infty) (iv) none of these

The function f(x)=1/(1+x^2) is decreasing in the interval (i) (-infty,-1) (ii) (-infty,0) (iii) (1,infty) (iv) (0,infty)

Consider the equation log_2 ^2 x- 4 log_2 x- m^2 -2m-13=0,m in R. Let the real roots of the equation be x_1,x_2, such that x_1 < x_2 .The set of all values of m for which the equation has real roots is (i) (-infty ,0) (ii) (0,infty) (iii) [1, infty) (iv) (-infty,infty)

Let f^(prime)(x)>0 AA x in R and g(x)=f(2-x)+f(4+x). Then g(x) is increasing in (i) (-infty,-1) (ii) (-infty,0) (iii) (-1,infty) (iv) none of these

For which interval the given function f(x)=2x^3-9x^2+12x+1 is decreasing? a) (-2,infty) b) (-2,1) c) (-infty,-1) d) (1,2)

The function f(x)= [x(x-2)]^2 is increasing in the set a) (-infty,0) cup (2,infty) b) (-infty,1) c) (0,1)cup(2,infty) d) ( 1 , 2 )

The value of x for which the function given by f(x)=2x^3-3x^2-12x+12 is increasing lies in: a) (-infty,-1)cup(2,infty) b) (-infty,-4)cup(2,infty) c) (-infty,0)cup(2,infty) d) (-infty,-2)cup(2,infty)

The solution set of the inequation ||x|-1| < | 1 – x|, x in RR, is (i) (-1,1) (ii) (0,infty) (iii) (-1,infty) (iv) none of these